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The HI Mass Function of the Local Universe: Combining Measurements from HIPASS, ALFALFA and FASHI

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read By combining HIPASS, ALFALFA, and FASHI into one 76%-sky sample processed with identical methods, this paper establishes the most complete local-universe HI mass function to date, including the first FASHI measurement.

desk verdict First FASHI HIMF and an ambitious three-survey combination, but the pooled 1/Vmax treatment underweights HIPASS and the quoted Omega_HI is biased. read the letter →

arxiv 2411.09903 v2 pith:KMHH5WZH submitted 2024-11-15 astro-ph.GA

Wenlin Ma , Hong Guo , Haojie Xu , Michael G. Jones , Chuan-Peng Zhang , Ming Zhu , Jing Wang , Jie Wang
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Peng Jiang
This is my paper · ORCID
classification astro-ph.GA
keywords HImassfunctionlocaluniverseHIPASSALFALFAFASHISchechtercosmicabundance1/Vmaxmethod
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to measure how many galaxies of each neutral-hydrogen mass fill the local universe by pooling three blind HI surveys—HIPASS, ALFALFA, and the new FASHI catalogue—into a single $31{,}528$ square-degree sample covering 76% of the sky. To make the combination meaningful, the authors recalculate distances, completeness, and the mass function in exactly the same way for every survey. The payoff is a local HI mass function with cosmic variance strongly suppressed: a Schechter fit with low-mass slope $\alpha=-1.30$, knee mass $\log(M_s)=9.86$, and cosmic HI abundance $\Omega_{\rm HI}=4.54\times10^{-4}$. The paper also reports the first HI mass function from FASHI and finds that a double Schechter function with two knee masses fits the data better than a single one. If correct, this gives future HI surveys a local benchmark for the gas content of galaxies and how it evolves.

What carries the argument

The load-bearing machinery is a unified $1/V_{\max}$ estimator run on the merged sample. Each galaxy contributes weight $f_{\rm rms,i}/[C(S_{21,i}|W_{50,i})V_{\max,i}]$, where $C$ is the completeness from error-function fits to the $S_{21}^{3/2}\,dn/d\log S_{21}$ plateau in each line-width bin, $V_{\max}$ is the maximum volume in which the galaxy would still clear the 50% completeness limit, and $f_{\rm rms}$ is a pixel-level weight that corrects FASHI's uneven exposure. Distances come from the same Cosmicflows-4 model for all three surveys, and $V_{\max}$ is computed over the full $31{,}528\,\mathrm{deg}^2$ area. This uniformity is what lets the authors compare and then combine surveys with very different selection functions.

What would settle it

A uniform deep HI survey covering both hemispheres could measure the HI mass function separately in the north and south: if the two disagree by more than the quoted uncertainties below $10^9\,M_\odot$, the universal-HIMF premise fails. The no-evolution assumption could be tested directly by measuring the HIMF in the $0.042<z<0.05$ slice with a deep survey; a measured slope or amplitude change there would invalidate the HIPASS volume extension.

Watch

Extended reading notes

Core claim

Combining HIPASS, ALFALFA, FASHI north, and FASHI south at $0<z<0.05$ with all four samples reduced through one pipeline gives the most complete HI mass function of the local universe measured so far. A single Schechter fit to the total yields $\alpha=-1.30\pm0.01$, $\log(M_s/h_{70}^{-2}\,M_\odot)=9.86\pm0.01$, and $\phi_s=(6.58\pm0.23)\times10^{-3}\,h_{70}^3\,\mathrm{Mpc}^{-3}\,\mathrm{dex}^{-1}$, which integrates to $\Omega_{\rm HI}=(4.54\pm0.20)\times10^{-4}\,h_{70}^{-1}$. A double Schechter function with a shared slope and two knees at $\log(M_{s1})=9.96$ and $\log(M_{s2})=9.65$ fits better, with the reduced $\chi^2$ dropping from $56/17$ to $24/15$, especially improving the high-mass end. The authors interpret the differences between individual survey HIMFs at low masses as large-scale structure effects and argue that averaging over 76% of the sky suppresses cosmic variance enough to give an unbiased local estimate.

Load-bearing premise

The measurement assumes the intrinsic HI mass function is the same across the whole surveyed sky, so that averaging over regions with different large-scale structure recovers the true cosmic function; it also assumes no HI evolution between $z=0.042$ and $z=0.05$, which lets the HIPASS volume be extended to the common redshift limit.

Editorial extensions

If this is right

  • Future HI surveys can compare their deeper or higher-redshift measurements against a local benchmark that is not tied to one patch of sky.
  • The local cosmic HI abundance $\Omega_{\rm HI}\approx4.5\times10^{-4}$ provides an anchor for studies of HI evolution towards $z\sim0.2$.
  • The better-fitting double Schechter function implies that the local HI mass function may be shaped by two distinct galaxy populations, possibly centrals and satellites.
  • The individual survey HIMFs provide a direct measure of how much large-scale structure biases single-survey estimates at low HI masses.
  • The FASHI HIMF presented here is the first from that survey and can be updated as future FASHI releases cover more sky.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the universal-HIMF premise holds, the north/south differences seen in the individual surveys are pure sample variance and should shrink as deeper surveys cover more volume; if they persist, the combined function is an average of environmentally different HIMFs and its low-mass end is not a single universal curve.
  • The two Schechter knees around $10^{9.6}$ and $10^{10}\,M_\odot$ map naturally onto populations split by halo mass; a direct test would be to recompute the HIMF using only central or only satellite galaxies from a group catalogue.
  • The pixel-weighting correction for FASHI's uneven exposure is a template for other time-filler surveys whose depth varies across the sky.
  • Applying the same pipeline to future FASHI data releases, or to other all-sky HI surveys, would show how much of the remaining scatter is methodological rather than cosmic.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper presents the first HIMF measurement for the FASHI survey and combines HIPASS, ALFALFA, and FASHI (split into north and south) to derive a 'total' HIMF over 31,528 deg^2 at 0<z<0.05, claiming this is the most complete local HIMF to date. The authors apply a uniform distance framework (Cosmicflows-4), a common completeness treatment based on S21 and W50, and the 1/Vmax estimator. They fit the total HIMF with a single Schechter function (alpha=-1.30, log Ms=9.86, phi_s=6.58e-3, Omega_HI=4.54e-4) and also present a double-Schechter fit. The central claim is that combining the three surveys suppresses cosmic variance and yields an unbiased local HIMF.

Significance. If the central measurement is sound, this would be a valuable reference product: the first FASHI HIMF, a uniform re-analysis of three major HI surveys, and a nearly all-sky local HIMF. The completeness analysis is careful, and the agreement of the ALFALFA and FASHI plateau levels in Fig. 3 is a genuine cross-validation. The use of a consistent distance and completeness pipeline across all samples is a real strength. However, the current combination scheme in Sect. 3.3 is not the standard volume-weighted 1/Vmax combination, and this affects the headline HIMF and Omega_HI. The significance therefore depends on whether the Vmax treatment is corrected and the results re-derived.

major comments (2)
  1. [Sect. 3.3, Eq. (5) and Table 3] The sentence 'When combining the four samples, we calculated Vmax for each galaxy using the total sky area of 31528 deg2' is not a valid application of the 1/Vmax estimator for a union of surveys with disjoint footprints. A galaxy detected in HIPASS could not have been detected over the ALFALFA or FASHI footprints, so its maximum volume should be (Omega_HIPASS/4pi)*(4pi/3) D_max^3, not (Omega_total/4pi)*(4pi/3) D_max^3. Using the total sky area for every galaxy is algebraically equivalent to forming the sky-area-weighted average of the four sample HIMFs; indeed, the total values in Table 3 (e.g., log M_HI=9.5: 1.279e-2) match the area-weighted sum of the four sample entries. This is not the volume-weighted combination that gives the number density in the combined survey volume. Because HIPASS has the largest area (18,291 deg^2) but the shallowest depth, area-weighting overweights HIPASS relative to its volume share, pulling the combined HIMF down where HIPASS amplitudes are low. The authors should recompute each galaxy's Vmax using the sky area of its own survey and then combine the samples with volume weighting, or provide an explicit statistical justification for why the area-weighted average is the appropriate estimator for the cosmic HIMF. The fitted parameters in Table 4 and Omega_HI in Section 4 will likely change, and the quoted uncertainties do not capture this systematic.
  2. [Sect. 3.3, HIPASS redshift limit] The statement 'Since the HIPASS sample is limited to a slightly smaller redshift of z < 0.042, we can assume that there is no evolution within the redshift range of 0.042 < z < 0.05' is used to extend HIPASS Vmax to z=0.05. In the 1/Vmax method, Vmax is the volume actually surveyed in which a source could have been detected; HIPASS did not observe z>0.042. The no-evolution assumption only says the space density is the same in that interval; it cannot make unobserved volume available for detection. HIPASS galaxies with D_max > D(z=0.042) should have Vmax truncated at the survey redshift limit. The numerical impact is modest because HIPASS's flux limit gives D_max ~ 72 Mpc (z ~ 0.017) for a knee-mass galaxy, so only the highest masses (log M_HI >~ 10.65) are affected, but the reasoning is incorrect and the effect on the high-mass bin should be quantified explicitly.
minor comments (5)
  1. [Sect. 1, last paragraph] There is a typo: 'ALAFLFA' should be 'ALFALFA'.
  2. [Sect. 3.3, Eq. (5)] The definition of Vmax_i is not stated explicitly. Please add an equation or sentence defining Vmax_i = (Omega_survey/4pi) * (4pi/3) D_max^3 for each survey, and clarify the units and sky area used.
  3. [Table 3 caption] The table caption should state that the 'Total' column is the area-weighted combination of the four samples; if the method is revised after the major comment above, the caption and values will need to be updated.
  4. [Sect. 5.2] The phrase 'increasing MH i by 0.06 dex and decreasing phi by -0.09 dex' has a double negative; it should read 'decreasing phi by 0.09 dex'.
  5. [Sect. 4, double Schechter fit] The improvement in reduced chi-square from 56/17 to 24/15 is reported without a statistical significance test. A simple delta-chi-square or F-test probability would help support the claim that the double Schechter is preferred.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the HIMF is a direct 1/Vmax measurement from independent catalogs, and the Schechter fits and Omega_HI integral are transparent standard conversions, not fitted inputs relabeled as predictions.

full rationale

The central measurement is the 1/Vmax HIMF (Eq. 5), constructed directly from the three independent survey catalogs using per-galaxy completeness weights and maximum volumes. The completeness limits are derived from source counts via the S21-W50 plane, not from the HIMF itself. The Schechter fits are descriptive models applied to these measured points, and Omega_HI in Eq. (8) is explicitly presented as the integral of the best-fit Schechter function; this is a standard estimator, not a hidden circularity, because the fitted parameters are not being used to predict a quantity that was already an input. The double-Schechter comparison is model selection on the same data, which is not circular. The flagged assumption in Section 3.3 that HIPASS Vmax can be extended from z<0.042 to z=0.05 under a no-evolution assumption, and the use of the combined sky area of 31528 deg^2 for all Vmax calculations, are selection-function approximations and potential biases, but they are not definitional or self-referential. Self-citations to Guo et al. (2023) and Ma et al. (2024) appear in comparative or contextual statements and are not load-bearing for the derivation. No step reduces by construction to its own input, so the circularity score is 0.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central measurement rests on fitted completeness curves (broken power laws and error-function widths per survey), the FASHI rms-weighting polynomial, and the Schechter parameters used to summarize the HIMF and derive Omega_HI. It also relies on domain assumptions about the universality of the HIMF, the validity of the 1/Vmax estimator, the completeness model, and the CF4 distance field. No new physical entities are introduced.

free parameters (5)
  • Completeness broken power-law parameters (a1, a2, Wcut) per sample = HIPASS: 0.412, 1.528, 2.232; ALFALFA: 1.162, 2.400, 2.476; FASHI north: 1.219, 2.295, 2.150; FASHI south: 1.069…
    Fitted to the measured 50% completeness limits S21,50%(W50) via Eq. 4 and Table 2. These curves determine Vmax for every galaxy and therefore directly set the HIMF normalization and shape.
  • Completeness error-function width sigma_logS21 per sample = 0.139 (HIPASS), 0.113 (ALFALFA), 0.322 (FASHI north), 0.259 (FASHI south)
    Fitted in each W50 bin using Eq. 3. Used in the 1/C completeness weights in Eq. 5 to correct the HIMF for incompleteness above the 50% cut.
  • FASHI rms-noise weight polynomial coefficients = not reported
    A second-order polynomial is fitted to normalized galaxy surface density versus rms noise per 2 deg2 pixel (Fig. 2). The reciprocal weights frms are applied to all FASHI galaxies in Eq. 5 and pixels with weights outside 0.5-2 are discarded.
  • Single Schechter parameters (alpha, log Ms, phi_s) = -1.30, 9.86, 6.58e-3
    Best fit to the measured total HIMF (Table 4). These fitted values are used in Eq. 8 to compute Omega_HI.
  • Double Schechter parameters (phi_s1, Ms1, phi_s2, Ms2, alpha) = 2.67e-3, 10^9.96, 5.96e-3, 10^9.65, -1.24
    Best fit to the measured total HIMF, preferred by reduced chi2 (24/15 vs 56/17). The two knee masses are interpreted as separate galaxy populations.
assumptions (6)
  • domain assumption The HIMF is universal across the surveyed 76% sky, so sky-area-weighted averaging of sample HIMFs gives an unbiased cosmic HIMF.
    The combination scheme in Section 3.3 treats the four samples as independent draws from the same HIMF. The paper's own Fig. 5 shows factor-level differences between north and south at low mass, which are attributed to cosmic variance but could reflect true environmental dependence.
  • standard math The 1/Vmax estimator is unbiased within each survey volume when the selection function is known.
    Standard estimator from Schmidt (1968). The paper notes this method is sensitive to large-scale structure, which is the motivation for combining surveys to suppress cosmic variance.
  • domain assumption Completeness above the 50% limit is accurately described by the fitted error function C(S21|W50), so 1/C weighting corrects residual incompleteness.
    Section 3.2 and Eq. 3. The method assumes the galaxy surface density follows S^-3/2 for a complete sample and that the error function fit is valid between 50% and 100% completeness.
  • ad hoc to paper No evolution of the HIMF between z=0.042 and z=0.05, used to extend HIPASS effective volumes beyond the survey's observed redshift limit.
    Section 3.3 states: 'Since the HIPASS sample is limited to a slightly smaller redshift of z<0.042, we can assume that there is no evolution within the redshift range of 0.042<z<0.05.' This extends Vmax for bright HIPASS galaxies into a volume HIPASS did not observe.
  • domain assumption Distances from the Cosmicflows-4 Wiener filter model are accurate enough that residual distance errors do not bias the HIMF.
    Section 3.1 adopts the CF4 model for all three catalogues. Section 5.1 compares flow models and finds up to 0.08 dex distance differences at the low-mass end, which shifts M_HI by 0.16 dex but is deemed minor.
  • domain assumption HI masses follow the optically thin relation in Eq. 2 with negligible self-absorption.
    Standard relation from Meyer et al. (2017). Self-absorption is acknowledged as an unquantified systematic in the Introduction.

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Cite this review

Pith. "Pith review of The HI Mass Function of the Local Universe: Combining Measurements from HIPASS, ALFALFA and FASHI." pith.science (2026). https://pith.science/paper/KMHH5WZH

@misc{pith2026241109903,
  author       = {Pith},
  title        = {Pith review of: The HI Mass Function of the Local Universe: Combining Measurements from HIPASS, ALFALFA and FASHI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KMHH5WZH}},
  note         = {Machine review of arXiv:2411.09903}
}
read the original abstract

We present the first HI mass function (HIMF) measurement for the recent FAST All Sky HI (FASHI) survey and the most complete measurements of HIMF in the local universe thus far. We obtained these results by combining the HI catalogues from HI Parkes All Sky Survey (HIPASS), Arecibo Legacy Fast ALFA (ALFALFA) and FASHI surveys at redshift 0 < z < 0.05, covering 76% of the entire sky. We adopted the same methods to estimate the distances, calculate the sample completeness, and determine the HIMF for all three surveys. The best-fit Schechter function for the total HIMF shows a low-mass slope parameter of alpha = -1.30 and a knee mass log(Ms) = 9.86, along with a normalisation of phi_s = 0.00658. This gives us the cosmic HI abundance: omega_HI= 0.000454. We find that a double Schechter function with the same slope alpha better describes our HIMF, where the two different knee masses are log(Ms1) = 9.96 and log(Ms2) = 9.65. We verify that the measured HIMF is marginally affected by the choice of distance estimates. The effect of cosmic variance is significantly suppressed by combining the three surveys and this provides a unique opportunity to obtain an unbiased estimate of the HIMF in the Local Universe.

Figures

Figures reproduced from arXiv: 2411.09903 by the authors.

Figure 1
Figure 1. Angular distribution of H i sources in FASHI sky (orange area), ALFALFA sky (blue area), and HIPASS (yellow area) sky. Grey points indicate individual detections. As the sky coverage of FASHI survey is not uniform, we split it into several pixels, each with an area of 2 deg2 . In cases where there is an overlap between two surveys, we present the areas with deeper coverage [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Weights of FASHI north galaxies. Left panel: Blue line shows the normalised surface density as a function of the rms noise [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Distribution of S 3/2 21 dn/d log S 21 as a function of the flux density, S 21, where dn is the surface number density of galaxies in a given log S 21 bin. This relation is used to determine the completeness of H i targets for all three surveys in different W50 bins, following the practice of Haynes et al. (2011). For fair comparisons, the measurements in both ALFALFA and FASHI are limited to the redshift range of 0… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Distribution of FASHI north (top-left), FASHI south (top [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Left: H i mass functions of ALFALFA, HIPASS, and FASHI north and FASHI south, shown as blue, orange, red, and purple solid lines, respectively. The total HIMF by combining three surveys is shown as black open circles with error bars. Right: Best-fit Schechter function …
Figure 6
Figure 6. Figure 6: Total H i mass functions calculated by different distance estimate models. The pure Hubble Flow, flow model in Masters (2005), NAM model and CF4 model in Cosmicflow-4 (adopted in our work) are shown as blue, orange, red solid lines, and black open circles with their er…

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Forward citations

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